Chapter 2.6, Problem 14PSB

To determine

To find: supplement of complement of the angle.

Answer to Problem 14PSB

  ${165}^{\circ }$

Explanation of Solution

Given information: Four times the supplement of an angle is added to eight times its complement, the sum is ${540}^{\circ }$

Formula used: sum of two supplementary angle is ${180}^{\circ }$ and sum of two complementary angles is ${90}^{\circ }$ . Supplement of an angle $x^{\circ }$ is ${(180-x)}^{\circ }$ and complement is ${(90-x)}^{\circ }$ .

Calculation: let measure of the angle is $x^{\circ }$ then its supplement is ${(180-x)}^{\circ }$ and complement is ${(90-x)}^{\circ }$ . According to the given information.

  $\begin{array}{l}$ 4{(180-x)}^{\circ }+8{(90-x)}^{\circ }={540}^{\circ }$\therefore {720}^{\circ }-4x^{\circ }+{720}^{\circ }-8x^{\circ }={540}^{\circ }\\ \therefore 12x^{\circ }={900}^{\circ }\\ \therefore x^{\circ }={75}^{\circ }\\ \text{Supplement of its complement is}{180}^{\circ }-({90}^{\circ }-x)\\ ={180}^{\circ }-({90}^{\circ }-{75}^{\circ })\\ ={165}^{\circ }\end{array}$